Scientific notation – Grade 8 math lesson
Lesson 2 of 16 in the Grade 8 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 8 (ages 13–14) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Grade
- Grade 8 (ages 13–14)
- You need
- Paper, a pencil and this page
- Graded
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is graded straight away with a worked explanation, so you never have to grade anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “Why is 12 × 10⁵ not in standard form?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Writing 45 × 10³ as an answer. The front number must be less than 10: 4.5 × 10⁴.
- Giving 0.0036 the power +3. Small numbers have negative powers: 10⁻³.
Tip for home: Look up distances in space or sizes of tiny things and write them in standard form.
What your child will learn
Learning goal: write very large and very small numbers in scientific notation and calculate with them.
Success looks like
- I can write numbers in standard form.
- I can convert back to ordinary numbers.
- I can multiply and divide in standard form.
Key words
- power of ten
- 10 multiplied by itself, such as 10³ = 1,000
- exponent
- the small number showing the power
- negative power
- a power for numbers less than 1
- adjust
- rewrite so the front number is between 1 and 10
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Order the sizes of planets, cells and atoms written in standard form.
The big ideas (for the adult)
A number in scientific notation is A × 10ⁿ, where A is at least 1 and less than 10: 45,000 = 4.5 × 10⁴.
Small numbers have a negative power: 0.0036 = 3.6 × 10⁻³.
To multiply, multiply the front numbers and add the powers; then adjust so the front number is between 1 and 10.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Graded by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, graded by Classfern |
| Independent practice | 15 min | Graded by Classfern |
| Closure and exit ticket | 6 min | Graded by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are graded by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all graded instantly.
More practice
More Grade 8 math lessons
- Repeating decimals
- Laws of exponents
- Square roots and cube roots
- Simplifying expressions
- Solving equations
- Systems of equations
- Arithmetic and geometric sequences
- Linear functions and slope
- Functions
- Graphing functions
- Angle relationships
- Volume and surface area
- The Pythagorean theorem
- Transformations
- Scatter plots and lines of fit
Curriculum
Common Core State Standards 8.EE.A.4: “Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology”
Common Core State Standards 8.EE.A.3: “Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 10⁸ and the population of the world as 7 times 10⁹, and determine that the world population is more than 20 times larger.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.